Discrete low-discrepancy sequences
Combinatorics
2010-07-15 v3 Probability
Abstract
Holroyd and Propp used Hall's marriage theorem to show that, given a probability distribution pi on a finite set S, there exists an infinite sequence s_1,s_2,... in S such that for all integers k >= 1 and all s in S, the number of i in [1,k] with s_i = s differs from k pi(s) by at most 1. We prove a generalization of this result using a simple explicit algorithm. A special case of this algorithm yields an extension of Holroyd and Propp's result to the case of discrete probability distributions on infinite sets.
Cite
@article{arxiv.0910.1077,
title = {Discrete low-discrepancy sequences},
author = {Omer Angel and Alexander E. Holroyd and James B. Martin and James Propp},
journal= {arXiv preprint arXiv:0910.1077},
year = {2010}
}
Comments
Since posting the preprint, we have learned that our main result was proved by Tijdeman in the 1970s and that his proof is the same as ours